Unit 4 Probability Mid-Unit Flashcard

Front

What is the definition of independent events in probability?

Back

Two events A and B are independent if the occurrence of one does not affect the occurrence of the other. Mathematically, P(A and B) = P(A) * P(B).

Front

What does it mean for two events to be mutually exclusive?

Back

Two events A and B are mutually exclusive if they cannot occur at the same time. This means P(A and B) = 0.

Front

What is the formula for the probability of the union of two events?

Back

P(A or B) = P(A) + P(B) - P(A and B).

Front

If P(A) = 0.2 and P(B) = 0.3, what is P(A or B) if A and B are independent?

Back

P(A or B) = P(A) + P(B) - P(A and B) = 0.2 + 0.3 - (0.2 * 0.3) = 0.44.

Front

What is the probability of drawing an even number from a set of cards numbered 1-10?

Back

There are 5 even numbers (2, 4, 6, 8, 10) out of 10 cards, so P(even) = 5/10 = 1/2.

Front

What is the probability of drawing a number greater than or equal to 5 from a set of cards numbered 1-10?

Back

There are 6 numbers (5, 6, 7, 8, 9, 10) out of 10 cards, so P(>=5) = 6/10 = 3/5.

Front

What is the definition of mutually inclusive events?

Back

Mutually inclusive events are events that can occur at the same time. For example, drawing a card that is both red and a face card.

Front

If two events A and B are dependent, what does that imply about their probabilities?

Back

If A and B are dependent, the occurrence of A affects the probability of B. Mathematically, P(B|A) ≠ P(B).

Front

What is the probability of drawing two cards of the same color from a deck of cards without replacement?

Back

P(same color) = P(first card) * P(second card | first card). For example, if the first card is red, the probability of the second card being red is 25/51.

Front

What is the probability of drawing two cards numbered 1-10 that are both odd?

Back

There are 5 odd numbers (1, 3, 5, 7, 9). P(odd on first draw) = 5/10, P(odd on second draw | first odd) = 4/9. So, P(both odd) = (5/10) * (4/9) = 20/90 = 2/9.